Large-amplitude long wave interaction with a vertical wall |
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| Institution: | 1. IRPHE, Marseille, France;2. Institute of Applied Physics, Nizhny Novgorod, Russia;1. Université de Toulon, CNRS/INSU, IRD, MIO, UM 110, 83957 La Garde, France;2. Aix Marseille Université, CNRS/INSU, IRD, MIO, UM 110, 13288 Marseille, France;3. Institute of Applied Physics, Nizhny Novgorod, Russia;4. Nizhny Novgorod, State Technical University, Nizhny Novgorod, Russia;5. National Research University, Higher School of Economics, Russia;6. Institute for Analysis, Johannes Kepler University, Linz, Austria;1. State Key Laboratory of Hydro-science and Engineering, Tsinghua University, Beijing 100084, China;2. Collage of Engineering, Ocean University of China, Qingdao, Shandong 266100, China;1. Department of Mathematics, CSU Chico, Chico, CA, United States;2. Department of Mathematics, Emory University, Atlanta, GA, United States;3. Department of Mathematics, CSU Monterey Bay, Seaside, CA, United States;4. Institute of Mathematics and Mechanics, Kazan Federal University, Kazan, Russia |
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| Abstract: | The rigorous solution of the nonlinear shallow-water equations for the wave field near a vertical wall is derived; it is used to calculate the height of the water oscillations near the wall versus the height of the incident wave. This solution is used to find the exceedance probability of characteristics of the wave motion near the vertical wall. It is shown that the wave height and trough distributions of water oscillations near vertical structures are less than the Rayleigh distribution. Beside of this, the distribution of the crest heights exceeds the Rayleigh distribution (using normalization of the amplification factor for such geometry within the framework of the linear theory), and this explains the high frequency of freak wave events on breakwaters and coasts. |
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